# Sun-Planet Bevel

Planetary gear set of carrier and beveled planet and sun wheels with adjustable gear ratio, assembly orientation, and friction losses

**Libraries:**

Simscape /
Driveline /
Gears /
Planetary Subcomponents

## Description

The Sun-Planet Bevel gear block represents a carrier and beveled planet and sun wheels. The planet is connected to and rotates with respect to the carrier. The planet and sun gears corotate with a fixed gear ratio. You control the direction of rotation by setting the assembly orientation left or right. For model details, see Equations.

### Thermal Model

You can model
the effects of heat flow and temperature change by enabling the optional thermal port. To enable
the port, set **Friction model** to ```
Temperature-dependent
efficiency
```

.

### Equations

**Ideal Gear Constraints and Gear Ratios**

The Sun-Planet Bevel block imposes one kinematic and one geometric constraint on the three connected axes:

$${r}_{C}{\omega}_{C}={r}_{S}{\omega}_{S}\pm {r}_{P}{\omega}_{P}$$

$${r}_{C}={r}_{S}\pm {r}_{P}$$

where:

*r*is the radius of the carrier gear._{C}*ω*is the angular velocity of the carrier gear._{C}*r*is the radius of the sun gear._{S}*ω*is the angular velocity of the sun gear._{S}*r*is the radius of the planet gear._{P}*ω*is the angular velocity of the planet gear._{P}

The planet-sun gear ratio is defined as

$${g}_{PS}=\frac{{r}_{P}}{{r}_{S}}=\frac{{N}_{P}}{{N}_{S}},$$

where:

*g*is the planet-sun gear ratio. As $${r}_{P}>{r}_{S}$$, $${g}_{PS}>1$$._{PS}

*N*is the number of teeth in the planet gear._{P}*N*is the number of sun gear teeth._{S}

In terms of this ratio, the key kinematic constraint is:

$${\omega}_{S}={g}_{PS}{\omega}_{P}+{\omega}_{C}$$ for a left-oriented bevel assembly

$${\omega}_{S}=-{g}_{PS}{\omega}_{P}+{\omega}_{C}$$ for a right-oriented bevel assembly

The three degrees of freedom reduce to two independent degrees of freedom. The
gear pair is (1,2) = (*S*,*P*).

**Warning**

The planet-sun gear ratio, *g _{PS}*,
must be strictly greater than one.

The torque transfer is defined as

$${\tau}_{P}={\tau}_{loss}-{g}_{PS}{\tau}_{S},$$

where:

*τ*is the torque loss._{loss}*τ*is the torque for the sun gear._{s}*τ*is the torque for the planet gear._{p}

In the ideal case where there is no torque loss, *τ _{loss}* = 0. The resulting torque transfer equation is $${\tau}_{P}={g}_{PS}{\tau}_{S}$$.

**Nonideal Gear Constraints and Losses**

In the nonideal case, *τ _{loss}* ≠ 0. For more information, see Model Gears with Losses.

### Variables

Use the **Variables** settings to set the priority and initial target
values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

### Assumptions and Limitations

Gear inertia is assumed to be negligible.

Gears are treated as rigid components.

Coulomb friction slows down simulation. For more information, see Adjust Model Fidelity.

## Ports

### Conserving

## Parameters

## More About

## Extended Capabilities

## Version History

**Introduced in R2011a**